Vacuum cleaners of the type mentioned above are generally known, for example, from European patent EP 1 674 020 B1. In such vacuum cleaners, the dust is separated by vortex formation in the air that is mixed with dust and dirt. If the centrifugal forces are sufficient, only the lighter air passes through, while the heavier dust and dirt particles remain in the collecting bin of the cyclone separator. A drawback of such separators is that the fans employed do not instantly build up the volume flow needed for the vortex formation. The centrifugal forces needed for the dust separation are thus not present right away, as a result of which, during the switch-on phase, a large quantity of the picked-up dust and dirt particles enters the cyclone and reaches the after-filters which then become clogged, and the particles might even reach the fan or exhaust air filters that are located downstream from the fan.